Time-Optimal Model Predictive Control for Linear Systems with Multiplicative Uncertainties

TL;DR

This paper introduces a time-optimal MPC approach for linear systems with multiplicative uncertainties, utilizing matrix-zonotope bounds for efficient online computation and ensuring finite-time convergence.

Contribution

It develops a novel MPC scheme that handles multiplicative uncertainties efficiently using offline computed bounds and adaptive terminal constraints.

Findings

Reduces online computational load through offline bounding set calculations.

Ensures recursive feasibility and finite-time convergence.

Demonstrates effectiveness in satellite orbital rendezvous simulation.

Abstract

This paper presents a time-optimal Model Predictive Control (MPC) scheme for linear discrete-time systems subject to multiplicative uncertainties represented by interval matrices. To render the uncertainty propagation computationally tractable, the set-valued error system dynamics are approximated using a matrix-zonotope-based bounding operator. Recursive feasibility and finite-time convergence are ensured through an adaptive terminal constraint mechanism. A key advantage of the proposed approach is that all the necessary bounding sets can be computed offline, substantially reducing the online computational burden. The effectiveness of the method is illustrated via a numerical case study on an orbital rendezvous maneuver between two satellites.